Matthieu Faessel

Segmentation of 3D microtomographic images of granular materials with the stochastic watershed

Segmentation of 3D images of granular materials obtained by microtomography is not an easy task. Because of the conditions of acquisition and the nature of the media, the available images are not exploitable without a reliable method of extraction of the grains. The high connectivity in the medium, the disparity of the objects shape and the presence of image imperfections make classical segmentation methods (using image gradient and watershed constrained by markers) extremely difficult to perform efficiently. In this paper, we propose a non‐parametric method using the stochastic watershed, allowing to estimate a 3D probability map of contours. Procedures allowing to extract final segmentation from this function are then presented.

Computational material design of filled rubbers using multi-objective design exploration

The rubber materials of tires contain nano-fillers i.e. carbon black and silica for the improvement of tire performances. The mechanical properties of filled rubber depend on the morphology of fillers. In this work multi-objective design exploration (MODE) is applied to material design of filled rubbers to get the information between mechanical properties and morphological design variables. A multi-scale random model based on a Poisson point process is used to generate a simulation model of filled rubber, and FFT (fast Fourier transform) based scheme is applied to solve large-scale dynamic viscoelastic simulation. To get big data including Pareto solution for data mining, multi-objective genetic algorithm are conducted on TSUBAME, supercomputer at Tokyo Institute of Technology. Data mining is employed to highlight properties-sensitive features in the microstructure. First, the volume fraction of bound rubber plays a major role in the material design of filled rubbers. Second, the radius of aggregates contributes to mechanical properties of filled rubbers. with resolution 2.13 nm per pixel. The slices of material probed by the microscope have a thickness around 40 nm. The first task is to segment these images, in order to identify the spatial distribution of the fillers as shown in Figure 1. An efficient way to keep track of the information embedded in the segmented images is to rely on a morphological characterization of the material. In this work, the covariance and the granulometry of fillers are used as feature value of morphology. The covariance and the cumulative granulometry curve of silica fillers are shown in Figure 2. Using the covariance and the granulometry curves, we can select parameters for the identification of multi-scale random models as explained in the next section. This is important way to merge the information between real material and simulation model at a material design stage. 2.2 Multi-scale random model A multi-scale random model is used to describe the microstructure (Figliuzzi et al. 2016) as shown in Figure 3. The first scale corresponds to the aggregates, while the second one describes more specifically the single particles inside the aggregates. In addition, several alternatives can be considered to locate the aggregates outside of the exclusion polymer. Bound rubber in Figure 3 is the interface layer between polymer and filler. Morphological parameters of a multi-scale random model are followings; ・ Poisson point intensity and volume fraction of exclusion polymer, ・ Poisson point intensity and radius of aggregate, ・ Poisson point intensity or volume fraction and radius of filler, ・ Overlapping distance of fillers, ・ Thickness of bound rubber. These parameters can be used as design variables for parametric study, optimization and MODE. For example, cross sections of six 3D simulation models generated by multi-scale random modeling are shown in Figure 4. These models are generated with different Poisson point intensity and radius of aggre(a) (b) Figure 1. (a) Original TEM image of silica filled rubber, (b) segmented binary image showing the filler in white. Figure 2. Covariance (solid line) and cumulative granulometry (broken line) computed from TEM image shown in Figure 1. (a)